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Companies that restate earnings change CFOs much more frequently than non-restating companies do, according to a study by two University of Alabama professors. But exactly how much more frequently turns out to be a matter of some confusion.

The report, titled “Corporate Governance Consequences of Accounting Scandals: Evidence from Top Management, CFO, and Auditor Turnover,” found that nearly a 10 percentage point gap exists between the adjusted turnover rate for finance chiefs at companies reporting lower earnings in a restatement (50.4 percent), compared to CFOs at non-restating companies (40.46 percent). Among CEOs, the difference using the same “regression model” was 14 percent (46.17 percent versus 31.73 percent).

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Perhaps more surprising is the calculation that audit firms are no more likely to be replaced by a company that restates than by a non-restating company, according to the report, which was drafted in March and last revised this month by professors Anup Agrawal and Tommy Cooper, of the university’s Culverhouse College of Business.

Some readers of the report, however, have paid more attention to the raw statistics, before the adjustment, showing that 65 percent of finance chiefs depart companies after restatements, and that 53 percent of CEOs depart under the same circumstances. “If you are a manager, chief financial officer or auditor working for a company that comes out with a restatement, start looking for another job. That’s the only conclusion you can draw” from the new study, observed Leon Gettler, a business journalist for Australia’s The Age newspaper, writing for the www.soxfirst.com corporate-finance Website.

(When contacted by CFO.com, Gettler conceded in an email that, after the departure levels at the control group were registered, the 10-point and 14-point actual departure-rate differentials for CFOs and CEOs are less impressive than the numbers on which he had based his comment. “But the bottom line is that their position is less secure post restatement,” he responded. “And if the market reaction to the restatement is severe, it would be even less secure because the board wants to be seen as doing something. Sacking the CEO or CFO is one way of achieving that.”)

Among non-restating companies in the study’s control group — again following the raw numbers — 43 percent of CFOs and 34 percent of CEOs were replaced during the period studied, while overall turnover involving members of top management measured 59 percent. The University of Alabama professors explain in the report, however, that to give a fair comparison of turnover, they needed to apply “logistic regressions that control for other determinants of management turnover.” That calculation includes the normal turnover rate for non-restating firms.

“Our study focuses on two important outcomes of the functioning of internal governance mechanism, namely management and auditor turnover, during a time of intense corporate turmoil,” they write in the study. They note the disruption in corporate accounting that followed the scandals involving Enron, WorldCom, Tyco International, HealthSouth and other companies, and the resulting reforms of the Sarbanes-Oxley Act of 2002.

An email from Prof. Cooper, responding to CFO.com’s request for information about the study, offered yet another set of numbers to explain how much more often CFOs and CEOs leave a company within a year of a restatement. Applying the differential of 10 percentage points for CFOs and 14 percentage points for CEOs in the adjusted numbers, the professor said, a restatement on average “increases the probability of CFO turnover by…24.6 percent…over the usual probability of turnover for CFOs of non-restating firms.” For CEOs, the probability of turnover increases a whopping 45.5 percent.

“The effects are even larger for sub-samples (of companies) where the misstatements were more egregioius,” Prof. Cooper added in his email.

Diluting the results for today’s finance executives under any scenario, however, could be the time period of restatements covered in the study: 1997 and 2002, before the great wave of post-Sarbanes-Oxley restating began to sweep the nation.

There were 919 restatements by U.S. public companies during the five-year period studied, according to the General Accountability Office. The research included 518 of them. After the steady rise in restatements that started in 2002, however, companies made a record 1,420 restatements in 2006 alone, according to a report earlier this year by investor research firm Glass, Lewis & Co., which predicted that the number might be at least as high this year.

The 2006 total was more than 12 times higher than in 1997, and last year represented one of every 10 public companies. In 2002, the first year of Sarbox, there were 330 restatements. Plus, in an April review by CFO, various experts noted that in the post-Sarbox years restatements — often involving inadvertent errors rather than fraud — have been more accepted as a result of the complexity of the system.

The Alabama study by Profs. Cooper and Agrawal does discuss a number of factors to be considered when examining CFO and CEO turnover, as well as the replacement of auditors post-restatement.

Some companies change CFOs or CEOs to regain “reputational capital” that may have been lost, to limit liability from possible classs-action lawsuits, or to help reverse market-value losses.

“On the other hand, there are also reasons why an earnings restatement may not lead to greater management turnover,” the report says. They include the high cost in human capital that may result from replacing executives, and difficulties with internal controls if key individuals are dismissed, “unless the [accounting] problems are directly linked to those individuals.” Further, if the reputational damage is judged to be minor, “the net benefits from replacing managers can be small.”

The benefits associated with replacing the auditor also reflect whether a company needs to “regain its lost reputational capital or limit its liability exposure.” Those costs can be large, however, and may include dealing with “steep learning curves” in replacing an auditor, and complications associated with the narrow choice among audit-firm candidates, especially when the field contains certain industry specialties.

But perhaps the most significant lesson of the study is that a careful reading of academic reports is always warranted.